MAYBE
Input TRS:
      1: le(0(),y) -> true()
      2: le(s(x),0()) -> false()
      3: le(s(x),s(y)) -> le(x,y)
      4: minus(0(),y) -> 0()
      5: minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
      6: if_minus(true(),s(x),y) -> 0()
      7: if_minus(false(),s(x),y) -> s(minus(x,y))
      8: gcd(0(),y) -> y
      9: gcd(s(x),0()) -> s(x)
      10: gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
      11: if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
      12: if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))
      13: rand(x) ->= x
      14: rand(x) ->= rand(s(x))
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Uncurrying le
      1: le^1_0(y) -> true()
      2: le^1_s(x,0()) -> false()
      3: le^1_s(x,s(y)) -> le(x,y)
      4: minus(0(),y) -> 0()
      5: minus(s(x),y) -> if_minus(le^1_s(x,y),s(x),y)
      6: if_minus(true(),s(x),y) -> 0()
      7: if_minus(false(),s(x),y) -> s(minus(x,y))
      8: gcd(0(),y) -> y
      9: gcd(s(x),0()) -> s(x)
      10: gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
      11: if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
      12: if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))
      13: rand(x) ->= x
      14: rand(x) ->= rand(s(x))
      15: le(0(),_1) ->= le^1_0(_1)
      16: le(s(_1),_2) ->= le^1_s(_1,_2)
Number of strict rules: 12
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #if_gcd(true(),s(x),s(y)) -> #gcd(minus(x,y),s(y))
     #2: #if_gcd(true(),s(x),s(y)) -> #minus(x,y)
     #3: #if_gcd(false(),s(x),s(y)) -> #gcd(minus(y,x),s(x))
     #4: #if_gcd(false(),s(x),s(y)) -> #minus(y,x)
     #5: #if_minus(false(),s(x),y) -> #minus(x,y)
     #6: #gcd(s(x),s(y)) -> #if_gcd(le(y,x),s(x),s(y))
     #7: #gcd(s(x),s(y)) -> #le(y,x)
     #8: #minus(s(x),y) -> #if_minus(le^1_s(x,y),s(x),y)
     #9: #minus(s(x),y) -> #le^1_s(x,y)
     #10: #le(s(_1),_2) ->? #le^1_s(_1,_2)
     #11: #le^1_s(x,s(y)) -> #le(x,y)
     #12: #le(0(),_1) ->? #le^1_0(_1)
Number of SCCs: 3, DPs: 7
  SCC { #10 #11 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: [1,2]	p: 1	w: max(x1 + 1, x2 + 1144)
      le	s: [1]	p: 4	w: max(x1 + 28102)
      le^1_s	s: [1]	p: 4	w: max(x1 + 28102)
      s 	s: [1]	p: 1	w: x1
      #le	s: [1,2]	p: 1	w: max(x1 + 1, x2 + 1144)
      #le^1_0	s: 1
      minus	s: 1
      gcd	s: []	p: 3	w: max(x1 + 28384, x2 + 28384)
      false	s: []	p: 2	w: 28101
      true	s: []	p: 0	w: 28102
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 0
      #if_minus	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
      #minus	s: [2]	p: 0	w: max(x2 + 1)
      le^1_0	s: []	p: 4	w: 28102
      if_minus	s: 2
      if_gcd	s: []	p: 3	w: max(x1 + 282, x2 + 28384, x3 + 28384)
      #if_gcd	s: [2]	p: 0	w: max(x2 + 1, x3 + 1)
      #gcd	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
    Removed DPs: #11
Number of SCCs: 2, DPs: 5
  SCC { #5 #8 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      #le^1_s	s: [1,2]	p: 1	w: max(x1 + 1, x2 + 1144)
      le	s: [1]	p: 4	w: max(x1 + 28103)
      le^1_s	s: [1]	p: 4	w: max(x1 + 28103)
      s 	s: [1]	p: 1	w: x1
      #le	s: [1,2]	p: 1	w: max(x1 + 1, x2 + 1144)
      #le^1_0	s: 1
      minus	s: 1
      gcd	s: []	p: 3	w: max(x1 + 37049, x2 + 37049)
      false	s: []	p: 2	w: 28101
      true	s: []	p: 0	w: 28103
      rand	s: []	p: 0	w: x1 + 1
      0 	s: []	p: 1	w: 0
      #if_minus	s: [2]	p: 5	w: max(x1 + 2, x2 + 28105, x3 + 28102)
      #minus	s: [1]	p: 5	w: max(x1 + 28105, x2 + 28102)
      le^1_0	s: []	p: 4	w: 28103
      if_minus	s: 2
      if_gcd	s: []	p: 3	w: max(x1 + 8946, x2 + 37049, x3 + 37049)
      #if_gcd	s: [2]	p: 0	w: max(x2 + 1, x3 + 1)
      #gcd	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
    Removed DPs: #5
Number of SCCs: 1, DPs: 3
  SCC { #1 #3 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.